Q1a: Is the master key password created per DB instance?
A1a: Assuming the question really means "Is the master key created per DB?"" then answer is Yes. Each DB has an different master key. there is also a thing called the service master key, which is per SQL Server instance.
Q1b: When I backup that DB (.bak) will I be able to restore the DB to
another Server2?
A1b: Yes. The master key in the restored database can be open using the original password. Then the Server2 service master key encryption can be added to the restored DB master key.
Q2: Do I need to backup the certificate, master key or symmetric key
if I want to restore to another server?
A2: No. All these objects are part of the database and they are restored along with the database. Specific needs to backup individual keys may arise from operational requirements (eg. key escrow).
Q3: When should the symmetric key be opened?
A3: Keys that require opening have to be opened in the session. Once opened, they stay open until explicitly closed or until the session disconnects. An 'open' key is 'open' only in the session that opened it.
Q4: Should I worry about who can open and close the symmetric key? ...
A4: Now this is the real question. You have two alternatives really, which correspond to two distinct scenarios:
Scenario A: when the service needs to access encrypted data without asking the user for passwords to the data. This is the vast majority of the cases. In this case the service needs to open the keys somehow. the solution is that the SQL Server uses the service master key to encrypt the database master key and the database master key is used to encrypt the certificate's private key and the private key is used to encrypt a symmetric key and the symmetric key encrypts the data. The SQL Server itself can reach any data following this chain, because it has access to the service master key. In this case the data is cryptographically protected only against accidental media loss: a lost laptop with the database on it, or an improperly disposed HDD with database of backup files on it etc. For all other threats, the data is not cryptographically protected, is only protected by the access control: since the SQL Server itself can decrypt the data w/o needing a password from the user, any user with sufficient privileges can access the data w/o knowing the password. In other words, a compromised ASP application may allow access to the encrypted data. As a note, scenarios in which the root of encryption is some secret stored on the ASP web application itself are just a (badly designed) variation on this and do not change anything.
Scenario B: when the service requires the user to provide a password. The password must come from the end user. In a web application, the user must type the password in a form in the browser, it gets sent over SSL channel to the ASP application, which passes it to the SQL Session (again on an SSL channel) and SQL can now decrypt the data using this password. This scenario is typical for multi-tenant applications in which tenants provide the data access password. In this scenarios the data is cryptographically secured against unauthorized access, because the SQL Server itself, nor the intermediate ASP web application, simply do not know the password. Even for a syadmin user with all privileges it would be impossible to read the data. Data can be moved at will and remains just as unscrutable, as it can be, again, only be read by the end-user that has knowledge of the password at the root of the encryption chain. Note that any 'shortcut' deviation in this scenario in which the password is 'saved' somewhere intermediately and not provided by the end-user this scenario degrades immediately to the first Scenario A.
A mandatory read for you: Encryption Hierarchy.
It will depend on the type of data being access and your company's security requirements/policy. In general you do not want users sharing an account, especially if that account has more than read permissions on your database. I would verify with your security folks or legal group if there are any specific requirements for managing access to data, or with auditing. If you fall under any industry standards like HIPPA or PCI they have controls that require being able to map access to a particular user.
With regards to how you allow users to run reports that is usually driven by policy where I have worked. Do you experience any performance issues now with how they are pulling reports and "peak" at data? As a DBA, I'm a control freak to a certain degree, I like to know who and what is making calls to my data. I have been in one environment where reports were pointed to a database snapshot of the production database, so their was less of a performance concern. Another environment it was not until their report caused a performance issue in production that we would tell them if you want that information run it after business hours.
Best Answer
Although I am not an expert, I will suggest reading the following article on the c-sharp corner:
https://www.c-sharpcorner.com/article/implement-column-level-encryption-decryption-in-sql-server-2016/
This details the process fairly well and has some working examples posted in a way that i feel might suit your application.